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Abstract
In this paper, the design of an efficient illuminator for extreme ultraviolet (EUV) applications such as photolithography, metrology, and microscopy is investigated. Illuminators are arrangements of optical components that allow us to tailor optical parameters to a targeted application. For the EUV spectral range, illuminators are commonly realized by an arrangement of several multilayer mirrors. Within this publication, design methods are developed to tailor optical parameters such as the intensity distribution, the spatial coherence, and the spectral bandwidth by using only one multilayer mirror. For the demonstration of the methods, an illuminator is designed for a compact in-lab EUV interference lithography system that is suited for industrial EUV resist qualification and large-area nanopatterning. The designed illuminator increases the wafer-throughput and improves the imaging quality.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
The demand for sources of extreme ultraviolet (EUV) radiation increases with the number of novel industrial and scientific applications at these wavelengths, such as photolithography [1–4], metrology [5], and microscopy [6,7]. In state-of-the-art industrial radiation sources, a plasma emits the desired EUV radiation. Specifically, plasma-based EUV sources can be separated into two different types, depending on the generation mechanism of the plasma. In discharge-produced plasma (DPP) EUV sources, the plasma is generated by an electrical discharge that ionizes the fuel gas [8–10], whereby in laser-produced plasma (LPP) EUV sources, the plasma is generated by a pulsed laser evaporating a solid or liquid target [11–13]. The resulting EUV radiation is emitted into a spherical or hemispherical solid angle, typically within a broad spectral range. Depending on the application in which the DPP and LPP EUV sources are used, illuminators are necessary to match the emitted radiation to the requirements of the desired application.
Beam guidance and shaping of EUV radiation can be only achieved by using reflective or diffractive optical elements since the transmission of EUV radiation is limited so that refractive optical elements cannot be employed. Reflective optical elements such as grazing incidence optics enable high reflectance by utilization of the total external reflection [14]. However, due to the required low grazing incidence angle for total external reflection, several design limitations arise. Diffractive optical elements (e.g., Fresnel optics or multilayer mirrors), on the other hand, offer a high flexibility regarding different incidence angles or spectral and angular reflectance, being highly suitable to realize optics for EUV radiation [15]. In contrast to Fresnel zone plates, multilayer mirrors enable an efficient use of the EUV radiation over a specific angular and spectral range, which can be tuned by optimizing the layer structure [16].
Multilayer mirrors consist of a substrate coated with high-Z and low-Z materials alternately, where Z is the atomic layer number. Each boundary between these layers causes a slight partial reflection of the incident radiation. If these partial reflected rays are in phase, high reflectance will occur for a certain wavelength within a constrained spectral and angular range [14]. Due to the strong absorption that occurs in the EUV wavelength range, the possible number of utilized multilayer optics to still enable high-efficiency operation of the overall system is very limited. For many applications, the designed optics accordingly need to fulfill many tasks simultaneously, and multilayer mirror design must carefully consider the layer system and mirror’s shape to enable the desired spectral filtering properties as well as beam guidance and shaping.
Fig. 1. Schematic representation of the developed design method for illuminators for partially coherent radiation in the extreme ultraviolet.
This paper presents the design methods of tailored illuminators for partially coherent EUV sources. For the demonstration of the methods, an optimized illuminator is designed for a compact in-lab EUV interference lithography system to increase its productivity and its imaging quality while maintaining the necessary degree of spatial coherence. The presented methods and obtained results are considered for a certain lithographic application but also hold for other applications in metrology and microscopy. Hence, the methods can be applied to numerous cases, where coherent or partially coherent sources are utilized.
2. DESIGN METHOD
Most illuminators for the EUV spectral region are arrangements of multilayer mirrors that are designed to tailor the source radiation to a desired application, whereby each multilayer mirror is optimized to fulfill one or multiple specific functions. For example, illuminators could be realized by several multilayer mirrors to adjust the intensity distribution over an angular and spatial range or by a single multilayer mirror to collimate the radiation from the source. As mentioned before, multilayer mirrors can form the incident radiation within a constrained spectral and angular range. To enable certain spectral filter properties as well as beam guidance and beam shaping, a precise investigation of different multilayer coatings is necessary. The procedure to design a multilayer mirror is divided into the following steps (see Fig. 1):
- 1. Basic beam path design
- 2. Multilayer system design by recursive algorithm
- 3. Sequential raytracing
- 4. Non-sequential raytracing
In general, optical elements can be used to tailor the optical field regarding the aimed application. Hereby, an increased number of elements increases the degree of freedom for adjusting the optical parameters. A small number of optical elements is often preferable in EUV design, however, as the overall optics transmission is higher due to lower absorption losses.
Depending on the number of optical elements and geometrical restrictions by the used experimental setup, first an appropriate beam path is determined schematically. The basic geometry of optical elements and the resulting optical parameters can be deduced with ABCD matrix formalism [17], a formalism based on matrix multiplication, which enables a simple determination of the paraxial optical properties and can, therefore, be applied to estimate the diameter and curvature of suitable multilayer mirrors. Furthermore, it is possible to determine the relation between the spatial coherence length and the usable solid angle of the source. The spatial coherence length is the length scale within which rays from the source maintain interference properties. This directly depends on the opening angle of the source since a higher opening angle leads to a larger angular range of the emitted radiation. The relation between the opening angle of the source and the spatial coherence length can be deduced by a schematic approach (see Fig. 2). The emitted radiation can be described by a chief and a marginal ray. The marginal ray is defined by the (full) opening angle of the source ${\theta _{\rm{NA}}}$. The used optical system, in this case the illuminator, is modeled by the two principal planes, input $H$ and output ${H^\prime}$.
A coherent angle ${\theta _{\rm{coh}}}$ is defined, in which coherent rays are projected into the mask plane. The relation between the spatial coherence length ${l_s}$ in the image plane and the (full) opening angle of the source ${\theta _{\rm{NA}}}$ is deduced by geometrical considerations leading to
where $y$ is the (full) spot size diameter in observation plane (mask size for the lithographic application). The coherent angle ${\theta _{\rm{coh}}}$ can be expressed by [14] where $\lambda$ is the exposure wavelength and ${r_{\rm{source}}}$ is the radius of the emitting radiation volume of the source (the so-called emission pinch). This leads to the following relation between the spatial coherence length ${l_s}$ and the opening angle ${\theta _{\rm{NA}}}$ of the source:If the field size and the source radius are considered as constant (fixed magnification), a higher opening angle leads to a lower spatial coherence length in the image plane. As the intensity is proportional to the squared opening angle of the source, $I \propto {\theta _{\rm{NA}}}^2$, this leads to a trade-off between the usable intensity and the spatial coherence length, which cannot both be optimized at the same time.
Fig. 2. Schematic representation of the relationship between the source opening angle ${\theta _{\rm{NA}}}$ and the coherence length in the mask plane ${l_s}$. ${\theta _{\rm{coh}}}$ is the coherent angle, ${r_{\rm{source}}}$ is the source radius, and $y$ is the spot size diameter in the image plane.
The structural analysis of multilayer coatings can be executed by various approaches. In this paper, the recursive method is used, which links the reflection coefficients ${r_{j,j + 1}}$ of a subsequent layer boundary with a previous one ${r_{j - 1,j}}$, where $j = 0,1,\ldots,n$ (see Fig. 3) [18]. According to the Fresnel equations, the reflection coefficient for the $\sigma$ and $\pi$ polarization (with electric field perpendicular and parallel to the plane of incidence, correspondingly) is given by
After the multilayer system is designed, the beam path is calculated by a sequential raytracing analysis to identify the right curvature or shape of the multilayer mirrors in both dimensions. There are numerous software packages available for this computation [19,20]. All packages are based on the discretization of the radiation field by rays to which are attributed a certain amplitude, phase, and corresponding area. Furthermore, the rays are divided by their reflected and refracted components, which are caused by an alternating change of the layer material. The entirety of all sorted rays yields to radiation fields that collectively lead to the reflected radiation by the multilayer mirror. After optimization of the multilayer shape, the designed multilayer system needs to be adjusted iteratively due to the changed incidence angles on the mirror surface.
In the last step, the resulting intensity distribution formed by the illuminator is calculated by non-sequential raytracing. By optimization of the curvature and shape of the multilayer mirror, a plane field illumination of the mask in a lithographic application can be achieved, which subsequently leads to low wavefront errors.
3. PHOTOLITHOGRAPHY SETUP
In this paper, an illuminator consisting of a single multilayer mirror is designed for an EUV interference lithography system called the EUV laboratory exposure tool (EUV-LET) [21]. A single multilayer mirror configuration guarantees a low loss of radiation due to the limited reflectance of multilayer mirrors within the EUV range. The EUV-LET is a compact nanopatterning tool designed for the qualification of industrial photoresists and allows the realization of sub-30 nm periodic nanostructures by using the achromatic Talbot approach [22], with a potential resolution limit in the sub-10 nm range [23,24]. The imaging process is based on the interference of diffraction orders that arise by the illumination of a transmission mask consisting of periodic line structures or hole arrays. The interference effect requires a coherent illumination over a few periods of the mask pattern, which consequently leads to the requirement of a spatial coherence length along the periodic structures [25]. Furthermore, polychromatic illumination of periodic structures leads to a stationary self-image (demagnified copy of the illuminated mask structure) after a certain propagation distance called the achromatic Talbot distance, which depends on the spectral bandwidth. Finally, the intensity and the homogeneous intensity distribution on the periodic structure are important parameters influencing the wafer-throughput and pattern fidelity within an exposure field. The developed lithographic setup consists of following main components (see Fig. 4):
- • DPP EUV source, which provides a plasma pinch with a diameter of 340 µm [at full width at half-maximum, (FWHM)] [26]
- • Aperture to avoid stray light and an out-of-band (OoB) filter [27]
- • Multilayer mirror (illuminator) for in-band filtering and capturing of defined solid angle [28]
- • Transmission mask to generate a high contrast intensity modulation [22]
- • Photoresist coated wafer for transfer of the intensity modulation into a height profile
- • Charge-coupled device (CCD) camera to monitor the beam position
Table 1. Requirements on the Designed Illuminator and Resulting Trade-Offs
The illuminator of the recent setup is realized by a plane multilayer mirror. This leads to an intensity of ${0.1}\;{\rm{mW/c}}{{\rm{m}}^2}$ in the mask plane for an operation frequency of 2.5 kHz of the DPP EUV source. In addition, a mask area of ${{2}} \times {{2}}\;{\rm{mm}}^2$ can be illuminated by a homogeneous intensity distribution with an intensity level above 90% compared to the maximum intensity in the center of the field [28]. The relative spectral bandwidth at $\lambda = {13.5}\;{\rm{nm}}$ is 3.6%, and the spatial coherence length is calculated to 26.8 µm in the mask plane [14].
For increasing the wafer-throughput (in ${\rm mm}^2/ \min$ for a resist with a given sensitivity), an optimized multilayer mirror is designed that will replace the current flat multilayer mirror shown in Fig. 3. To achieve a high wafer-throughput, either the intensity in the wafer plane (leads to shorter exposure times) or the exposure spot size in sample plane (larger patterned area) can be increased. The optimized multilayer mirror shall improve the industrial usability of the EUV-LET. For that reason, different requirements are set to fulfill this goal (see Table 1). Important optical parameters for the EUV-LET are the intensity, homogeneously illuminated area, exposure wavelength, spectral bandwidth, and spatial coherent length in mask plane. These quantities are partially counteracting; for example, for a given pulse energy, increasing the intensity counteracts against the spatial coherence length or spectral bandwidth. While designing the illuminator, these trade-offs must be carefully evaluated to find an optimum solution.
4. RESULTS AND DISCUSSION
In a first step, the basic illuminator design is selected. For the chosen lithographic application, the collected EUV radiation from the source has to be collimated on the transmission mask to enable a plane field illumination and subsequently a high contrast of the forming self-images of the mask pattern. To additionally minimize intensity loss in the lithographic setup, an illuminator consisting of only one optical element is chosen. Based on these requirements, the precise shape of the illuminator is later designed with the raytracing method. The available intensity and resulting spatial coherence length for the single, collimating illuminator is calculated by the basic geometrical approach given in Section 2. According to Eq. (3), the spatial coherence length in the mask plane can be displayed as a function of the source opening angle (numerical aperture) (see Fig. 5). Since the intensity is proportional to the squared numerical aperture of the source, the trade-off between the intensity and the spatial coherence length in the mask plane can be seen. In general, there is no optimum value for both parameters. For the given lithographic application, the spatial coherence length should not be below 20 µm to still achieve a reasonable distance window for the lithographic process (achromatic Talbot lithography) [21]. As a result, the source opening angle can only be increased by a factor of 1.34 relative to the current plane mirror design, which subsequently leads to an intensity increase in the mask plane by a factor of 1.8.
Fig. 5. Dependency of the spatial coherence length on the opening angle of the utilized plasma EUV source.
A similar trade-off for the intensity and spectral bandwidth dependences is obtained when the multilayer coating is designed by applying the recursive method algorithm. For the multilayer mirror, alternating layers of Mo and Si are used, and the material data are taken from CXRO database [29]. An important parameter of multilayer mirrors is the angle of incidence, which is defined in this paper as an angle between the tangent to the mirror surface and the incident beam. The angle of incidence, where the reflectance of the multilayer mirror gets maximized, is called the Bragg angle, analogous to an x ray reflection on crystal planes [30]. For multilayer mirrors with fixed bilayer thickness and thickness ratio, the intensity increases for near-normal incidence angles designs, while the spectral bandwidth and the degree of polarization decrease simultaneously (see Fig. 6).
Fig. 6. Simulations results of the recursive method for multilayer coatings. Dependency of the peak reflectance at $\lambda = {13.5}\;{\rm{nm}}$ (black curve), the relative spectral bandwidth (gray curve, left), and the degree of polarization (gray curve, right) on the Bragg angle. The Bragg angle of 60° as used for the addressed lithographic application is indicated by a red dashed line.
Fig. 7. Angular (left) and spectral (right) reflectance profile of the optimized multilayer coating on a flat substrate.
For the given application, it is sufficient to optimize only the relative spectral bandwidth since the angular bandwidth can be neglected due to the small usable opening angle of the source. Since the individual Bragg angle is determined by the structure of the multilayer coating, e.g., the number and thickness of the individual coating layers, each Bragg angle corresponds to another multilayer system. One can see that a high Bragg angle near normal incidence (90°) leads to highest peak reflectance and reasonable relative spectral bandwidth. Since in a real laboratory setup some geometrical limits arise from the size of the vacuum housing and setup geometries, a Bragg angle near normal incidence cannot be used in single-mirror configurations. In the presented lithographic setup, the maximum possible Bragg angle is 60°, which leads to a maximum unpolarized peak reflectance of 59% and a relative spectral bandwidth of 5% (FWHM) as it has been calculated for a multilayer structure with a bilayer period of 8.1 nm, a bilayer ratio $\Gamma$ of 0.376, and a number of 40 bilayers. The degree of polarization is 22.7%, and the angular bandwidth is 5.6°.
To analyze the performance of the multilayer system, the angular and spectral reflectance profiles for the designed mirror are plotted (see Fig. 7). The low grazing incidence angles in the angular spectrum (Fig. 7, left) correspond to the total external reflection. At the designed grazing angle of 60°, the Bragg reflection occurs. For the spectral reflectance (Fig. 7, right), peak reflectance occurs at $\lambda= {13.5}\;{\rm{nm}}$ while other wavelengths are suppressed by the bandpass filter characteristic of the multilayer coating. The resulting illumination spectra of the utilized DPP EUV sources after spectral filtering by the currently used and the optimized layer system show an increase of the integrated reflectance by a factor of 1.7 (see Fig. 8). Note that in both cases plane mirrors are simulated since the curvature of the mirror is optimized in a subsequent step.
Fig. 8. Illumination spectrum after spectral filtering by the current and the optimized multilayer system.
The computed main optical parameters and the layer design of the multilayer mirror are then used for the raytracing analysis, where the shape of the illuminator is optimized to achieve plane field illumination, which will lead to the highest illumination quality. The raytracing is performed with the software package OpticStudio 20.1 (version: January 21, 2020) from Zemax. A sequential analysis is used for the determination of the mirror shape while a non-sequential analysis is performed to display the intensity distribution and the wavefront in the image plane. For both parts of the analysis, the optical elements are defined by surfaces. For the sequential analysis, the order of layers is important since the paths of the rays are traced from one surface to another in a fixed order. After defining the different surfaces of the illuminator, the shape is optimized, resulting in different illuminator designs. For the optimization of the shape, two models are chosen. First, the standard surface of OpticStudio is used, which allows the definition of different radii of curvature or conicities. Furthermore, Chebyshev polynomial surfaces up to the 10th order are used. Both models show that an off-axis parabolic collimator is most suitable for the given application. To achieve highest collimation quality, the wavefront error is optimized. In this application, the plasma pinch of the DPP EUV source lies in the focal plane of the parabolic collimator so that the emanating rays from the focal point are transformed into parallel rays, which are guided onto the transmission mask. Since the pinch length is sufficiently small with respect to the distance between source and illuminator, the lateral extension of the pinch can be neglected. The illuminator shape is optimized to focus an incoming parallel ray into a point for the geometrical extensions given by the experimental setup (incidence angle of 60° and optical path length ${\lt}{{2}}\;{\rm{m}}$; see Fig. 9). For an optimized shape, the illumination spot on the mask is simulated by the non-sequential mode before and after the multilayer reflection (see Pos. 1 and Pos. 2 in Fig. 9, left), and the wavefront error of the intensity distribution is calculated. A low wavefront error corresponds to a near plane field illumination of the mask in the lithographic application. This enables high quality self-images of the mask pattern, which are formed behind the mask. For the optimized collimator the wavefront error (rms), the mask plane is calculated to ${1.1} \times {{1}}{{{0}}^{- 3}}$ waves, compared to 6.5 waves for the current plane mirror. The designed illuminator enables a homogeneous intensity distribution at mask plane over the considered patterned mask field of ${{4}} \times {{4}}\;{\rm{mm^2}}$ (see Fig. 10). In comparison to the spot before the multilayer mirror reflection, the phase is homogeneous over the full spot area. The optimized geometrical parameters of the designed illuminator can be found in Table 2. Computations with the non-sequential mode additionally show that the off-axis parabolic collimator is insensitive against medium-scale misalignments, e.g., misalignments of ${{\pm 10}}\;{\rm{mm}}$ and ${{\pm 2}}^\circ$ still lead to wavefront errors below 1 wave.
Fig. 9. Left, schematic representation of the designed illuminator and the resulting beam path with indicated positions 1 and 2 used for the beam analysis. Right, close-up on the CAD representation of the designed illuminator in OpticStudio with multilayer condition and simulated rays.
Fig. 10. Simulation results of the raytracing analysis for position 1 and 2 (see Fig. 9, left). The obtained spot from the illuminator generates a homogenous intensity distribution and phase over the considered patterning field of ${{4}} \times {{4}}\;{\rm{mm}}^2$.
The designed off-axis parabolic multilayer mirror, thus, increases the intensity and homogenous illuminated area in mask plane. This leads to a higher throughput of the EUV-LET to enhance the usability for industrial applications such as the photoresist characterization. Additionally, a plane field illumination of the mask can be realized, which leads to a higher imaging quality in the lithographic application.
5. CONCLUSION AND OUTLOOK
This paper presents the procedure of designing tailored illuminators for partially coherent EUV sources. The applied methods and obtained results are demonstrated by an illuminator, which is designed for a photolithography system for industrial resist qualification and large-area patterning, whereby an existing illuminator that is not optimized is replaced by the designed illuminator of this paper. The designed illuminator consists of an off-axis parabolic multilayer mirror, which increases the intensity by a factor of 3.06 due to collection of a larger solid angle and an optimized layer system. Additionally, a nearly plane field illumination (rms wavefront error ${\sim}{1.1} \times {{1}}{{{0}}^{- 3}}$) of an area of more than ${{4}} \times {{4}}\;{\rm{mm^2}}$ is achieved, while the spatial coherence length and the relative spectral bandwidth are matched to 20 µm and 3% at $\lambda = {13.5}\;{\rm{nm}}$, respectively. The designed off-axis parabolic multilayer mirror, therefore, increases the productivity and the imaging quality of an EUV photolithography system, enhancing its usability for industrial applications. Although the presented methods and obtained results are considered for a specific photolithography system, they can be used to tailor the illuminator to different wavelengths, bandwidths, or spot sizes. The methods consequently work also for other applications such as EUV metrology and microscopy.
Funding
Deutsche Forschungsgemeinschaft (DA 990/4-1).
Acknowledgment
This work was realized by cooperation activities in the frame of the Jülich Aachen Research Alliance for Fundamentals of Future Information Technology (JARA-FIT).
Table 2. Geometrical Parameters of the Optimized Off-Axis Parabolic Multilayer Mirror
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available in [29].
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